TY - JOUR
T1 - Spanning configurations and matroidal representation stability
AU - Pawlowski, Brendan
AU - Ramos, Eric
AU - Rhoades, Brendon
N1 - Publisher Copyright:
© (), (). All Rights Reserved.
PY - 2020
Y1 - 2020
N2 - Let V1,V2,… be a sequence of vector spaces where Vn carries an action of Ϭn for each n. Representation stability describes when the sequence Vn has a limit. An important source of stability arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some topological space X. We replace these configuration spaces with the variety Xn,k of spanning configurations of n-tuples (ℓ1,…, ℓn) of lines in ℂk with ℓ1 +… + ℓn = ℂk as vector spaces. That is, we replace the configuration space condition of distinctness with the matroidal condition of spanning. We study stability phenomena for the homology groups Hd(Xn,k) as the parameter (n, k) grows. We also study stability phenomena for a family of multigraded modules related to the Delta Conjecture.
AB - Let V1,V2,… be a sequence of vector spaces where Vn carries an action of Ϭn for each n. Representation stability describes when the sequence Vn has a limit. An important source of stability arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some topological space X. We replace these configuration spaces with the variety Xn,k of spanning configurations of n-tuples (ℓ1,…, ℓn) of lines in ℂk with ℓ1 +… + ℓn = ℂk as vector spaces. That is, we replace the configuration space condition of distinctness with the matroidal condition of spanning. We study stability phenomena for the homology groups Hd(Xn,k) as the parameter (n, k) grows. We also study stability phenomena for a family of multigraded modules related to the Delta Conjecture.
KW - representation stability
KW - subspace configuration
KW - symmetric group module
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M3 - Article
AN - SCOPUS:85146178051
JO - Seminaire Lotharingien de Combinatoire
JF - Seminaire Lotharingien de Combinatoire
IS - 84
M1 - 57
ER -